Space of modular forms of level 1740, weight 2, and Character 1740.g

• Label: 1740.2.g
• Level: $1740$
• Weight: $2$
• Character orbit: 1740.g
• Rep. character: $\chi_{1740}(349,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1740, [\chi])\).

	Total	New	Old
Modular forms	372	28	344
Cusp forms	348	28	320
Eisenstein series	24	0	24

Trace form

28 * q - 4 * q^5 - 28 * q^9 + 16 * q^11 + 8 * q^19 - 16 * q^21 + 4 * q^25 - 8 * q^31 - 12 * q^35 + 8 * q^39 + 8 * q^41 + 4 * q^45 - 28 * q^49 - 8 * q^51 + 24 * q^55 - 24 * q^59 - 40 * q^61 + 20 * q^65 + 24 * q^69 + 8 * q^71 + 16 * q^75 - 16 * q^79 + 28 * q^81 - 8 * q^85 - 40 * q^89 - 16 * q^91 + 8 * q^95 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1740, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1740.2.g.a	$1740$	$2$	1740.g	5.b	$2$	$2$	$2$	$13.894$	\(\Q(\sqrt{-1}) \)	None		✓			1740.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
1740.2.g.b	$1740$	$2$	1740.g	5.b	$2$	$2$	$2$	$13.894$	\(\Q(\sqrt{-1}) \)	None		✓			1740.2.g.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
1740.2.g.c	$1740$	$2$	1740.g	5.b	$2$	$12$	$12$	$13.894$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1740.2.g.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)
1740.2.g.d	$1740$	$2$	1740.g	5.b	$2$	$12$	$12$	$13.894$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1740.2.g.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{9}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1740, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)